Most Popular
1500 questions
6
votes
2 answers
Is it possible to have a trace fidelity of 1 even if two unitary operations are different?
The gate fidelity of two quantum unitary operations is often described using $\frac{1}{2^n}|\text{tr}(U^\dagger V)|$. Is it ever possible that $U^\dagger V \ne I$ however $\frac{1}{2^n}|\text{tr}(U^\dagger V)| = 1$? Specifically, is it possible to…
smi
- 163
- 6
6
votes
3 answers
Is there a rank-1 POVM on qubits with $4$ outcomes that is not extremal but such that its resulting shape on the Bloch sphere has a non-zero volume?
Let us consider a rank-1 POVM acting on qubits with $4$ outcomes (that is, all its elements are rank-1). Furthermore, let us assume that this POVM is unbiased, meaning that $\mathrm{Tr}\left[M_i\right]=\frac12$ for all $i\in[4]$. In particular, it…
Tristan Nemoz
- 8,694
- 3
- 11
- 39
6
votes
2 answers
What exactly are "quantum rotors"?
The Wikipedia entry on the subject is rather short. I am also curious about generalizations of quantum rotors in n-dimensions. An introductory explanation with at least one resource for further reading would be greatly appreciated.
user820789
- 3,440
- 14
- 43
6
votes
1 answer
Do the Towers of Hanoi admit any perfect state transfer?
The Towers of Hanoi is an old puzzle that involves moving $n$ discs of different radii among $k$ pegs, requiring each stack of discs to be monotonically increasing along the stack. Conventionally $n=6$ or so and $k=3$; it's also often studied in…
Mark Spinelli
- 15,789
- 3
- 26
- 85
6
votes
2 answers
Why do completely positive maps satisfy ${\rm Tr}[\Psi(\rho)_++\Psi(-\rho)_+]\leq{\rm Tr}[\Psi(\rho_+)]+{\rm Tr}[\Psi((-\rho)_+)]$?
I am studying a paper of M. Plenio, "Logarithmic Negativity: A Full Entanglement Monotone That is not Convex", PRL 2005 [arXiv:quant-ph/0505071].
In the paper, I do not fully understand the Eq.$(7)$. He said that
Employing linearity of operation…
Acpil
- 61
- 2
6
votes
2 answers
Why does the partial transpose of an entangled state have at most one negative eigenvalue?
I came over this unclear claim which i wondered someone could clarify:
"The partial transpose of an entangled state has at most one negative eigenvalue."
I wondered if this holds for all states or just some, searched around but couldn’t find some…
Pink Elephants
- 335
- 1
- 8
6
votes
2 answers
Are quantum simulators like Microsoft Q# actually using quantum mechanics in their chips?
Unlike Google's Bristlecone or IBM's Qbit computer, do simulators like Q# or Alibaba really use quantum mechanics anywhere in their physical chips? Are they just defining properties using a classical computer and trying to achieve quantum…
Yashank
- 263
- 1
- 4
6
votes
1 answer
Does the need of many quantum algorithms to be repeated several times impair the efficiency gains?
As I understand so far, in some algorithms such as Simon's algorithm, swap-test algorithm or quantum k-means algorithm, we repetitively perform a measurement yielding a classical result. Consequently, this pushes us to run the whole algorithm again…
Aman
- 473
- 3
- 13
6
votes
0 answers
Quantum Belief Propagation decoding
I have been reading about a family of quantum error correction codes called Quantum Turbo Codes, which are the quantum analog of the well-known classical Turbo codes. This codes were introduced in quantum serial turbo codes and the…
Josu Etxezarreta Martinez
- 4,246
- 17
- 43
6
votes
1 answer
Why no $Z$'s in the $\operatorname{F} (\sum_{j=0}^{n-1} 2^j Z_j) \operatorname{F}^\dagger$ operator?
An interesting numerical observation is that an operator defined as $\phi=\sum_{j=0}^{n-1} 2^j Z_j$ upon a QFT is rotated into an operator $\pi=\operatorname{F} \phi \operatorname{F}^\dagger$ which does not have any Pauli $Z$'s in its expansion. Is…
mavzolej
- 2,291
- 10
- 18
6
votes
2 answers
Just want to confirm: Do two CNOT gates cancel each other?
I see somewhere that this happens:
But I wonder if this is just identity.
Ka Wa Yip
- 171
- 3
6
votes
1 answer
Efficient method to find square root of a Hamiltonian
I'm working with a Hamiltonian $H$ represented as a linear combination of Pauli strings:
$$H = \sum_j \alpha_j P_j,$$
where $P_j \in \{I, X, Y, Z\}^{\otimes n}$ are tensor products of Pauli matrices and $n$ is the number of qubits.
I'm looking for…
Kushagra Garg
- 63
- 4
6
votes
2 answers
Is there a tool that can give you the unitary representing a quantum circuit from just a string?
Say I have a string representing the operations of a quantum circuit.
I want to have the unitary operator representing it.
Is there a tool for doing so in Python or else?
cnada
- 4,852
- 1
- 9
- 22
6
votes
2 answers
How do we code the matrix for a controlled operation knowing the control qubit, the target qubit and the $2\times 2$ unitary?
Having n qubits, I want to have the unitary described a controlled operation.
Say for example you get as input a unitary, an index for a controlled qubit and another for a target.
How would you code this unitary operation?
cnada
- 4,852
- 1
- 9
- 22
6
votes
2 answers
Incorrectly Calculating Probability Amplitudes for 3-qbit Circuit
I’m trying to calculate the probability amplitudes for this circuit:
My Octave code is:
sys = kron([1; 0], [1;0], [1;0])
h = 1/sqrt(2) * [1 1; 1 -1];
c = [1 0 0 0; 0 1 0 0; 0 0 0 1; 0 0 1 0];
op1 = kron(h, eye(2), eye(2));
op2 = kron(c,…
Sam Kennedy
- 71
- 3